# Generalized Clockwork Theory

## TL;DR

This paper extends the clockwork theory to include non-nearest neighbor interactions, non-abelian symmetries, and explores its embedding in supergravity, revealing new symmetry breaking patterns, mass spectra, and connections to the cosmological constant.

## Contribution

It introduces a generalized framework for clockwork theory with broader interactions, non-abelian groups, and supergravity embedding, expanding its theoretical and phenomenological scope.

## Key findings

- Mass spectrum of modes is altered with additional interactions.
- A single massless mode remains despite generalized interactions.
- Clockwork direction aligns with a specific SUSY breaking direction.

## Abstract

We generalize the clockwork theory in several directions. First, we consider beyond nearest neighbors interactions. Considering such interactions keeps a larger subgroup of the original $U(1)^{N+1}$ unbroken and can allow for different symmetry breaking patterns. We recover the original clockwork scenario in the presence of these additional interactions. In such case, the masses of the massive modes change, but a single massless mode remains intact. Such interactions are naturally interpreted as higher derivative terms from the point of view of extra dimensions. Second, we generalize the clockwork shift symmetry to non-abelian global groups. Third, trivial embedding of the clockwork scenario in supergravity, yields an AdS minimum as big as the clockwork interaction. Specifically, the clockwork is connected to the cosmological constant. We analyze the different ways in which a Minkowski supersymmetric minimum can be constructed, and demonstrate simple SUSY breaking mechanisms that preserve or break the clockwork symmetry. We show that the clockwork direction is actually a special SUSY breaking direction, that does not require the inclusion of additional fields or parameters. Fourth, we review the extra-dimensional origin of the mechanism and interpretation, in the case of conformal coupling to gravity.